Question

Suppose an economy has four​ sectors: Mining,​ Lumber, Energy, and Transportation. Mining sells

15​%

of its output to​ Lumber,

70​%

to​ Energy, and retains the rest. Lumber sells

5​%

of its output to​ Mining,

50​%

to​ Energy,

20​%

to​ Transportation, and retains the rest. Energy sells

10​%

of its output to​ Mining,

15​%

to​ Lumber,

30​%

to​ Transportation, and retains the rest. Transportation sells

10​%

of its output to​ Mining,

10​%

to​ Lumber,

60​%

to​ Energy, and retains the rest.

a. Construct the exchange table for this economy.

b. Find a set of equilibrium prices for this economy.

Answer 1

^ given above is the exchange table for the economy. Notice that the colums add up to 100%.

Assume prices pA, pB, pC, pD and quantities qA, qB, qC, qD for Mining, Lumber, Energy and Transport sectors respectively.

For simplicity, we can assume a numeraire good i.e. set price = 1 for a good, and think of it as a currency in terms of which other prices are quoted. Take pD = 1.

The basic constraint is Revenue generated by a sector must equal expenditure of that sector on purchases from other sectors.

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Solving,

^ in the absence of better (supply side) information, setting absolute quantities Qa = Qb = Qc = Qd was a necessary step.